I am trying to normalize a portfolio of equity options into Index terms, particularly the vega. For example, if I buy $1,000 vega each in MSFT and WFC, how much SPX vega can I sell vs this to be vega neutral. Obviously, two stocks won't provide enough correlation with the index to make this a vega neutral portfolio, but I'm looking for something that approximately tracks in a larger portfolio. My initial thoughts are a stock beta or vol beta adjustment. Since MSFT is ~ a 1 beta, I'd short $1,000 index vega vs it, whereas WFC is ~ a 1.5 beta, I'd short $1,500 index vega vs it.

Since nobody has responded, I will suggest the first thing that comes to mind in case it is useful.Your have a portfolio with market valueP = Sum_i N(i) C(i)where N(i) = number of contracts times 100 and C(i) = market price of option i (I write C for either put or call).Let's say the vega you want to hedge is the sensitivity of P to changes in some vol. associated to SPX --the ATM SPX vol. or VIX. Whatever it is, let's call it sigma_M. Now, even though we don't believe CAPM, maybe it's useful here as a first approximation, where it says:where sigma_i is a total vol. associated to stock i, beta_i is an estimate of the beta for stock i,and sigma(u_i) is an idiosyncratic vol. for stock i. Now, it is simply an exercise in partial derivatives to find: